X,Y相互獨(dú)立,且都服從[0,1]上的均勻分布 --> f(x,y)=1.
Z=X+Y
F(z)=P(x+y<z) = ∫∫f(x,y)dxdy = ∫∫dxdy =直線x=0,x=1,y=0,y=1,y=-x+z所圍面積
當(dāng)0<z<1時(shí), F(z) = (z^2)/2
當(dāng)1<z<2時(shí), F(z) = (z^2/2)-(z-1)^2
Z=X+Y的概率密度
f(z) = dF(z)/dz=z      0<z<1;  f(z) = 2-z     1<z<2.

卷積函數(shù)法:
f(x)=u(x)-u(x-1) --- 這里u是階躍函數(shù).(u(x)=1,x>0,=0,x<0)
f(y)=u(y)-u(y-1)
X,Y 獨(dú)立,Z=X+Y,所以f(z)是f(x)和f(y)的卷積.
f(z)=f(x)*f(y) --- * 是卷積.x處要帶入z.y處也要帶入z.
f(z)= (u(z)-u(z-1)) *(u(z)-u(z-1))
f(z) = z,當(dāng) 0<z<1; f(z) = 2-z,當(dāng) 1<z<2;
f(z) = 0,其余.